The 26-year-old moved to the Spanish capital club in 2015 and has struggled to get regular playing time under his belt, managing 24 appearances in all competitions. He is competing with Dani Carvajal and Nacho for a place in the starting lineup at Real.
Lack of playing time with the Champions League and the La Liga winners has seen him consider his future at Real. According to the Brazilian publication Globo Esporte, Danilo is attracting interest from several Premier League clubs.
However, the Blues are leading the race for his signature. The former FC Porto man has already agreed personal terms with the west London club who are in an advanced stage of negotiations for the defender.
Danilo, who turned 26 on Saturday, is targeting regular playing time in the 2017/18 season in order to improve his chances of making it to the Brazil squad for next summer's World Cup in Russia.
He believes a move to Chelsea will improve his chances of featuring regularly. The English champions' manager Antonio Conte has the services of Cesar Azpilicueta as the only recognised right-back in the squad.
The Spain international has been deployed on the right side of the three-man defence, with Victor Moses playing in the right wing-back position. Conte's side will return to the Champions League after a year of absence from the European competition.
Chelsea are looking at bolstering their squad this summer and the arrival of Danilo will strengthen their defence. The Stamford Bridge outfit have allowed John Terry and Nathan Ake to leave while completing the signing of Antonio Rudiger from AS Roma.
They have already signed three players in the ongoing transfer window. Willy Caballero was Chelsea's first signing as the goalkeeper arrived on a free transfer after being released from Manchester City.
Rudiger followed the Argentine stopper and Tiemoue Bakayoko became the club's latest addition. The France international arrived at the Bridge from AS Monaco. Should Chelsea manage to agree a fee with Real for Danilo, he is likely to become their fourth signing of this summer.